ILL GIVE BRAINLIEST
The coordinate grid shows points A through K. What point is a solution to the system of inequalities?
y < −2x + 10
y < 1 over 2x − 2
Answers
inequalities: y ≤ −2x + 10 & y > (1/2x) - 2 is a solution to the system of inequalities .
What does co ordinate math entail?
An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Definition of a coordinate plane.
An intersection of two perpendicular lines known as the x-axis and y-axis results in a 2D plane known as a coordinate plane.
The points which represents a the solution are: A, C, D and K
See the attached figure.
The given inequalities: y ≤ −2x + 10 & y > 1/(2x − 2)
The given points: A(-5,4), B(4,7), C(-2,7), D(-7,1), E(4,-2),
F(1,-6), G(-3,-10), H(-4,-4), I(9,3), J(7,-4) and K(2,3).
The attached figure represents the graph of the given inequalities.
The shaded area represents the solution of the inequalities.
So, the points lies in the shaded area represents the solution of the inequalities.
So, points A, C, D and K are a solution to the system of inequalities.
If the given inequalities: y ≤ −2x + 10 & y > (1/2x) - 2
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Related Questions
Justin Wallace started a business to offer development of online stores for small businesses. Record the following transactions in the journal of the business. Include an explanation with each journal entry
September 1 Wallace invested $32,000 cash in a business bank account to start his business. The business received the cash and gave Wallace owner's equity in the business
September 2 Purchased computer equipment on account, $9,800.
September 2
Paid cash for September's office rent of $3,900.
September 3 Recorded $6,400 revenue for services rendered to clients on account
Begin with the investment that Justin Wallace deposited in a business bank account.
September 1: Wallace invested $32,000 cash in a business bank account to start his business. The business received the cash and gave Wallace owner's equity in the business. Record the entry. (Record debits
first, then credits. Select the explanation on the last line of the journal entry table. Leave unused cells blank.)
Debit
Date
September 1:
Accounts :
Debit:
Credit:
Answers
On September 1 the debit and cash is as follows
Debit: Cash $32,000
Credit: Owner's Equity $32,000
How can we explain each statement?On September 1, Justin Wallace invested $32,000 cash into the business to start the business. This transaction increases the business's Cash account and increases the Owner's Equity account, which represents the owner's investment in the business.
September 2:
Debit: Accounts Payable $9,800
Credit: Cash $9,800
On September 2, the business purchased computer equipment on account for $9,800. This transaction increases the Accounts Payable account, which represents the business's obligation to pay the supplier, and decreases the Cash account.
September 2:
Debit: Cash $3,900
Credit: Rent Expense $3,900
On September 2, the business paid cash for September's office rent of $3,900. This transaction decreases the Cash account and increases the Rent Expense account, which represents the cost of renting office space.
September 3:
Debit: Service Revenue $6,400
Credit: Accounts Receivable $6,400
On September 3, the business recorded $6,400 revenue for services rendered to clients on account. This transaction increases the Service Revenue account, which represents the business's revenue from providing services, and increases the Accounts Receivable account, which represents the business's right to receive payment from clients for services rendered.
What is mensuration?Mensuration is the branch of mathematics that deals with the measurement of geometric shapes and figures, such as length, area, and volume. It typically includes the study of geometric shapes, such as circles, triangles, and polygons, and their properties, such as perimeter, area, and volume. Mensuration is used in many fields, including engineering, physics, and computer graphics.
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how many square feet of wallpaper will be used to cover a wall measuring 9 feet by 18 1/4 feet?
Answers
The area covered by the wallpaper will be 164.25 square feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, A wallpaper measures 9 feet by 18 1/4 feet.
Therefore, The area of the wallpaper will be,
= (9×73/4) square feet.
= 164.25 square feet.
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Choose all the expressions that equal 36.
Responses
A (14⋅32)2−28open paren 1 fourth times 32 close paren squared minus 28
B 23 + (58−54)2 + 122 3 + ( 58 - 54 ) 2 + 12
C 92 − (43 + 32) + 3005092 − ( 4 3 + 3 2 ) + 300 50
D 124 + (82 − 42) − 99124 + ( 8 2 − 4 2 ) − 99
E 53 − (2. 5 × 30) − 20
Answers
The expressions that equal 36 is:
E) 53 − (2. 5 × 30) − 20
Calculation of Algebra ExpressionEvaluated the mathematical expressions in each response to see if they equal 36.
A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.
B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.
C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.
D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.
Thus, only the expressions listed in my previous answer equal 36.
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The formula V = 1/3 πr²h gives the volume V of a cone with height h and base radius r.
Solve the formula for h.
Then find h when r = 2 inches and V = 45 cubic inches.
Answers
height = 10.74 inches
for steps refer attachment
The volume of a cone = (1/3) πr2h cubic units
Therefore, the volume of a cone = 20.93 cubic units
What is cone and formula?A cone has only one face, which is the circular base but no edges. A cone has only one apex or vertex point. The volume of the cone is ⅓ πr2h. The total surface area of the cone is πr(l + r) The slant height of the cone is √(r2+h2)Basically, the volume is equal to the product of the area and height of the shape. Volume = Base Area x Height. For shapes having flat surfaces such as cubes and cuboids, it is easy to find the volumeTo calculate the volume of a box, you need to know its height, width, and depth. You can find the volume by multiplying these three dimensions togetherTo learn more about cone refers to:
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[BRAINLIEST] The first two terms of a geometric sequence are 27 and 9. What is the fourth term?
Answers
The required Fourth term of the given geometric sequence is 1.
What is geometric sequence?Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbours.
A geometric sequence always multiplies (or divides) by the same number to move from one term to the next. Therefore, 1, 2, 4, 8, 16,... is geometric since each step is a multiple of two; 81, 27, 9, 3, 1, 31... is geometric since each step is a multiple of three.
According to question:Sequesnce; 27 , 9
Common ratio(r) = 9/27 = 1/3
Then, we know that
[tex]a_{n}=ar^{n-1}[/tex]
So,
a₄ = 27(1/3)³
a₄ = 27/27 = 1
a₄ = 1
Thus, fourth term of the sequence is 1.
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Answer:
1
Step-by-step explanation:
1 is the correct one i got it right on test
what percentage smoke something (cigars, cigarettes or both)? b. what percentage smoke neither cigars nor cigarettes? c. what percentage smoke cigars but not cigarettes? d. what is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?
Answers
Percentage is a concept used to express a fraction as a part of 100. It is typically expressed as a fraction with a denominator of 100 and is written as a number followed by the percent sign (%). For example, the fraction 3/20 can be expressed as 15%, which means 15 out of every 100. Percentage is a useful concept when comparing two or more values, as it provides a way to measure the relative size of each value. For example, if one group of people has 25% of the total number of votes, this means that they have more votes than the other groups, whose percentages are lower.
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Complete question:
A total of 28% of Americans smoke cigarettes, 7% smoke cigars and 5% smoke both cigarettes and cigars
a. What percentage smoke something (cigars, cigarettes or both)?b. What percentage smoke neither cigars nor cigarettes?c. What percentage smoke cigars but not cigarettes?d. What is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?what is the sum of all the elements from the first six rows of pascal's triangle?
Answers
The sum of all the elements present in the first six rows of the Pascal's triangle is equal to 63.
Pascal's triangle elements are represented by :
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Sum of all the elements of first six rows are:
First row : 1
Second row : 1 + 1 = 2
Third row : 1 + 2 + 1 = 4
Fourth row : 1 + 3 + 3 + 1 = 8
Fifth row : 1 + 4 + 6 + 4 + 1 = 16
Sixth row : 1 + 5 + 10 + 10 + 5 + 1 = 32
Sum of all the six row elements = 1 + 2 + 4 + 8 + 16 + 32
= 63
Therefore, the sum of all the elements of the first six row of Pascal's triangle is equal to 63.
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Write the equation of the line that passes through the points (−1,−7) and (1,7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answers
Use the equation y=mx+b where m is the slope and b is your y intercept.
Plug in one of the two sets coordinates into your equation y=7x+b. You should get 0 as your y intercept.
So you should end up with y=7x.
A patient took 400 mg of acetaminophen which ha the half life of 4 hour. How much acetaminophen will be in the patient in 4 hour? 2 hour? 1 hour?
Answers
If a patient took 400 mg of acetaminophen which has the half life of 4 hour, the amount of acetaminophen that will be in the patient is:
In 4 hour? 200 mgIn 2 hour? 100 mgIn 1 hour? 50 mgThe half-life of acetaminophen is 4 hours, which means that every 4 hours, half of the initial dose of 400 mg will still remain in the patient's body.
At 4 hours after taking the dose, the amount of acetaminophen in the patient's body would be:
400 mg / 2 = 200 mg
At 2 hours after taking the dose, the amount of acetaminophen in the patient's body would be:
400 mg / (2^(4/4)) = 200 mg / 2 = 100 mg
At 1 hour after taking the dose, the amount of acetaminophen in the patient's body would be:
400 mg / (2^(4/4)) = 100 mg / 2 = 50 mg
In conclusion, the amount of acetaminophen in the patient's body decreases by half every 4 hours.
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HELP ME PLEASE I DONT UNDERSTAND!!!!!
Answers
Explanation
The isosceles triangle shown shares congruent sides and congruent angles YZX and YXZ, both 25 degrees.
We know the triangle sum theorem says the angle sum = 180.
180 - 25 - 25 = 130 degrees
See attachment for help
show that 2 mn = 1 m (m n 2 ) 1 n (m n 2 ) and use this identity to obtain the unit fraction decompositions of 2 7, 2 35, and 2 91 as given in the 2/n table in the rhind mathematical papyrus.
Answers
The fractions found in the 2/n table in the Rhind Mathematical Papyrus.
2/7 = (m n 2 ) 1 n (m n 2 )
= (2 7 2 ) 1 7 (2 7 2 )
= (14 2 ) 1 7 (14 2 )
= 7 1 7 + 7 1 14
2/35 = (m n 2 ) 1 n (m n 2 )
= (2 35 2 ) 1 35 (2 35 2 )
= (70 2 ) 1 35 (70 2 )
= 35 1 35 + 35 1 70
2/91 = (m n 2 ) 1 n (m n 2 )
= (2 91 2 ) 1 91 (2 91 2 )
= (182 2 ) 1 91 (182 2 )
= 91 1 91 + 91 1 182
Using the identity (m n 2 ) 1 n (m n 2 ) we can decompose the fractions 2/7, 2/35, and 2/91 into unit fractions. For 2/7, we obtain the decomposition 7 1 7 + 7 1 14, for 2/35 the decomposition 35 1 35 + 35 1 70, and for 2/91 the decomposition 91 1 91 + 91 1 182. This matches the fractions found in the 2/n table in the Rhind Mathematical Papyrus.
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how to show that the real exponetial sequence for f[k]=f[kt] is f[k]b^k
Answers
The real exponential sequence for f[k]=f[kt] is f[k]=b^k.
What is exponential sequence ?
The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.
The real exponential sequence for f[k]=f[kt] can be shown to be f[k]=b^k by using the definition of exponential functions. If f[k]=f[kt], then f[k]=f[k-1]t and f[k-1]=f[k-2]t, and so on. By substitution, we have:
f[k]=f[k-1]t
f[k-1]=f[k-2]t
f[2]=f[1]t
f[1]=f[0]t
So we can write:
f[k]=f[k-1]t=f[k-2]t^2=...=f[1]t^(k-1)=f[0]t^k
Next, we can define b as f[0] and substitute it into the above equation:
f[k]=b^k
Therefore, the real exponential sequence for f[k]=f[kt] is f[k]=b^k.
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(x + 1) is a factor of x145 + 3x45 – 4.
True or False
Answers
(x + 1) is not a factor of the polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
We have a polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
If (x + 1) is a factor.
Then x = -1 is a zero of polynomial.
Now,
(-1)¹⁴⁵ + 3(-1)⁴⁵ - 4
= -8
Therefore, (x + 1) is not a factor.
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describe whether your percent yield for the product was high or low. if it was either high or low, explain what might have caused the high/low percent yield.
Answers
A product-focused process is commonly used to produce: high-volume, low-variety products.
There are other types of processes. This process is completely developed around the product, it is considered a continuous process with high volume of products that have low variety. It presents a high facility utilization (this is considered an advantage), organized by product, which receives a high-fixed price, but the variable cost is low.
Product focused prodction is one that focuses on improving the product by arranging sets of people into production lines to increase efficiency of production.
Equipment and people are grouped based on products being produced. For example in a manufacturing plant assembly lines are formed that focuses on one product.
This tends to be used for products that have low differentiation and are to be produced on high volume.
Example automobile plants, clothing factories, and food factories.
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an octahedron consists of two square-based pyramids glued together along their square bases to form a polyhedron with eight faces. imagine an ant that begins at the top vertex and walks to one of the four adjacent vertices that he randomly selects and calls vertex a. from vertex a, he will then walk to one of the four adjacent vertices that he randomly selects and calls vertex b. what is the probability that vertex b will be the bottom vertex? express your answer as a common fraction.
Answers
The probability that vertex b will be the bottom vertex will be 1/16
The ant has four equally likely possibilities for his initial step from the top vertex, each heading to one of the four vertices close to the top vertex.
When the ant reaches vertex A, he has four equally likely next steps, each heading to one of the vertices next to vertex A.
Only one of these possibilities, however, will send him to the bottom vertex: the one that brings him straight to the bottom vertex.
As a result, the ant's chance of reaching the bottom vertex after two steps is 1/4 * 1/4 = 1/16.
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Work out
(√6 +√12)²
Give your answer in the form
c+d√2
where c and d are integers.
Answers
Answer:
[tex]18 + \sqrt[12]{2} [/tex]
= 34.97056
formulas used to calculate the free cash flow to firm (fcff)?
Answers
(OCF): OCF = Net Income + Depreciation & Amortization - Changes in Working Capital, (CapEx): CapEx = Investment in Property, Plant & Equipment + Investment in Intangible Assets. therefore, (FCFF): FCFF = OCF - CapEx
The Free Cash Flow to Firm (FCFF) is a measure of a company’s cash flow available for distribution to shareholders and debt holders. To calculate FCFF, the following three steps are taken:
1. Calculate Operating Cash Flow (OCF): OCF is calculated by taking net income, adding back depreciation and amortization, and subtracting any changes in working capital.
2. Calculate Capital Expenditures (CapEx): CapEx includes investments in property, plant, and equipment, as well as any investments in intangible assets.
3. Calculate Free Cash Flow to Firm (FCFF): FCFF is calculated by subtracting CapEx from OCF. This figure represents the cash flow available for distribution to shareholders and debt holders.
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Identify the values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20.
(5,y1) and (x2,2)
Answers
The correct values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20 are,
⇒ y₁ = - 1
⇒ x₂ = 10
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The equation is,
⇒ 3x - 5y = 20
Now, If (5, y₁) is the solution of above equation, then it satisfy the equation.
⇒ 3x - 5y = 20
⇒ 3 × 5 - 5y₁ = 20
⇒ 15 - 5y₁ = 20
⇒ 15 - 20 = 5y₁
⇒ - 5 = 5y₁
⇒ y₁ = - 1
And, If (x₂, 2) is the solution of above equation, then it satisfy the equation.
⇒ 3x₂ - 5y = 20
⇒ 3x₂ - 5×2 = 20
⇒ 3x₂ - 10 = 20
⇒ 3x₂ = 20 + 10
⇒ 3x₂ = 30
⇒ x₂ = 10
Thus, The correct values that create ordered pairs that are solutions to the solutions to the equation are,
⇒ y₁ = - 1
⇒ x₂ = 10
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Suppose that 15 inches of wire costs 75 cents.
At the same rate, how much (in cents) will 9 inches of wire cost?
Answers
Answer: 45 cents.
Step-by-step explanation: We can find the cost per inch of wire by dividing the total cost by the total length of wire:
75 cents / 15 inches = 5 cents/inch
Now that we know the cost per inch, we can find the cost of 9 inches of wire by multiplying the cost per inch by 9:
5 cents/inch * 9 inches = 45 cents.
Answer:45 cents for 9 inches of wire
Step-by-step explanation:
Per every 5 incheses is 0.25 cents 0.75/15=$0.25 and then taking 0.25/5=$0.05 cents. So 1 inch costs 0.05 cents. So multiply 0.05×9=$0.45 cents. 45 cents
f(x)=x^4-4x^3 5 estimate local extrema of each function and estimate the intervals on which the function is increasing and decreasing
Answers
The local extrema is at point (3, -22).
The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).
Now, According to the question:
The function is :
[tex]f(x)=x^4-4x^3 +5[/tex]
Graphing Functions:
In order to graph a function, we first need to know the characteristics of that given function. On the other hand, we also need to simplify first the given function or rewrite it in general form for easier graphing.
Now, Graphing the function, we have
From the graph, the local extrema is at point (3, -22).
The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).
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A spinner with 7 equal sections
labeled A-G is spun 84 times. How
many times would you expect it to
land on a vowel?
Answers
Answer:
24 vowels
Step-by-step explanation:
A B C D E F G
two out of 7 are vowels....you would expect to get 2/7 ths of 84 spins to be vowels
2/7 * 84 = 24 vowels
In 2009 the average weekly wage of men exceeded that of a woman by $162. The um of their average wage equaled $1476. Write and olve a ytem of equation to determine the average wage of men and of women in 2009
Answers
The average wage of men is $819 and of women is $657 in 2009
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
M = W + 162M + W = 1476M = average wage of menW = average wage of womanTo solve this problem we must establish the equations according to the given data and solve the operations:
M = W + 162 (1)
M + W = 1476 (2)
We have two equations with two unknowns, substituting the value (M) in the second equation, we have:
M + W = 1476
W + 162 + W = 1476
162 + 2W = 1476
2W = 1476 - 162
2W = 1314
W = 1314/2
W = 657
Substituting (W) into one of the equations (M) we have:
M = W + 162
M = 657 + 162
M = 819
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Matt sells used books on the internet. The cost of using the website is $7.50 per week and he earns 1.50 on each book he sells Matt uses the linear model y=1.5x to figure his weekly earnings what is the rate of Change of this situation
Answers
Answer:
$1.5 per book
Step-by-step explanation:
Since y=1.5x, the rate of change is 1.5/1. Rate of change: y/x. Hence, the rate of change is 1.5/1 since y=1.5 and x=1.
1.5 / 1 = 1.5
Hence, the rate of change is 1.5.
But what's 1.5 represent?
1.5 is the number of dollars earned per book sold.
Hence, the rate of change is $1.5 per book.
Which could be the scale factor of the following similar figures? (1 point)
The first triangle's sides are 9,9,12
The second triangles sides are 6,6,8
A.) 2/3
B.) 3/4
C.) 1
D.) 3/2
E.) 4/3
Answers
Answer:3/2
Step-by-step explanation: just did the test
As all sides have grown by 2/3 times, The scale factor is 2/3. Thus, option A is correct.
What is scale factor?In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.
16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.
Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12
The corresponding sides are
6/9, 6/9, 8/12
When you simply, we get
2/3, 2/3, 2/3
As all sides have grown by 2/3 times, The scale factor is 2/3. Thus, option A is correct.
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Question 4 of 17:
Select the best answer for the question
4. Demand for winter holiday decorations is at an all-time high in late December. What may you consider after the holidays to make room for new spring
merchandise?
A. maintain an accurate count of all inventories
O B. all answers are correct
C. sell the holiday decorations at a discounted price
D. store decorations in the warehouse until next winter
Mark for review (Will be highlighted on the review page)
OO
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PAR
Answers
Answer:
Step-by-step explanation:
we will maintain an accurate count of all inventories.
so A is correct.
Is it
1.A
2.B
3.C
4.D
Answers
Answer:
26 R 1
Step-by-step explanation:
The number e is named after
?
Answers
list five vectors in span{1, 2 }. for each vector, show the weights on 1 and 2 used to generate the vector. do not make a sketch. V1 = ( 3 1 2 ) , V2 = ( −4 0 1 )
Answers
The five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)
We are given that two vectors
v1 = ( 3 1 2 ) and v2 = ( −4 0 1 )
We have to list five vectors in the span {v1, v2}
Let us choose five sets of weights as:
w = {0, 0}, {1, 0}, {0, 1}, {1, 1}, {1, -1}
So, the five vectors are:
V1 = 0 (v1) + 0 (v2) = (0 0 0)
V2 = 1 (v1) + 0 (v2) = (3 1 2)
V3 = 0 (v1) + 1 (v2) = (-4 0 1)
V4 = 1 (v1) + 1 (v2) = (3-4 1+0 2+1) = (-1 1 3)
V5 = 1 (v1) - 1 (v2) = (3+4 1-0 2-1) = (7 1 1)
Hence, the five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)
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suppose winston's loud music externalizes a cost onto his neighbor, chloe. suppose winston and chloe decide to solve this problem using the coase theorem. if they are successful, what is a possible result of the execution of this theorem?
Answers
The Coase theorem states that if property rights are well-defined and transaction costs are low, then the allocation of resources will be efficient, regardless of the initial allocation of property rights.
If Winston and Chloe successfully apply the Coase theorem to solve the problem of Winston's loud music externalizing a cost onto Chloe, they may reach a mutually beneficial agreement. This could result in either Winston reducing the volume of his music or compensating Chloe for the cost of the externalization, or a combination of both.
The goal is to reach a solution where the costs and benefits are more efficiently allocated between the two parties.
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Given: △ABC, D∈ AB , E∈ BC F∈ AC , DE ∥ AC , AD ∥ FE AD=6, DE=5, AB=17 Find: AC
Please help ASAP!
Answers
Answer: The length of AC is approximately 5.196 units.
Step-by-step explanation:
To find the length of AC, we can use the fact that DE is parallel to AC and AD is parallel to FE, which forms a pair of corresponding angles. Therefore, we can set up a proportion using the fact that corresponding angles are congruent.
DE/AC = AD/FE
We know that DE = 5 and AD = 6, so we can substitute these values into the proportion:
5/AC = 6/FE
We can cross-multiply and solve for AC:
5 * FE = 6 * AC
Next, using the fact that triangle ABC is a triangle, we can use the Pythagorean theorem to find the value of FE.
AB^2 + BC^2 = AC^2
17^2 + BC^2 = (AC)^2
289 + BC^2 = AC^2
Now, substitute the value of FE into the equation we have,
5 * sqrt(AC^2 - 289) = 6 * AC
multiply the both sides of the equation by the reciprocal of 5,
sqrt(AC^2 - 289) = (6/5) * AC
Square both sides of the equation,
AC^2 - 289 = 36/25 * AC^2
subtract the left side from the right side
-289 = -(36/25) * AC^2
divide both sides by -(36/25)
AC = sqrt(289/(1-(36/25)))
AC = sqrt(289/11/25)
AC = sqrt(289/275)
AC = sqrt(289/11)
AC = sqrt(26)
AC = approx 5.196152422706632
Therefore, the length of AC is approximately 5.196 units.
